HOMEWORK 4 – 2019
Exercise 1. Using the Mayer-Vietoris exact sequence compute the homology groups
of the sphere with two handles.
Exercise 2. Consider a surface which consists of the disk to which the Moebius band is
attached in such a way that we stick the boundary of the Moebius band (homeomorhic
to S1
) to the boundary of the disk. Using the Mayer-Vietoris exact sequence compute
the homology of this surface. (In fact, this is the projective plane.)
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